Reconstructing the three-dimensional (3D) geometry of object surfaces is essential for robot perception, yet vision-based approaches degrade under low illumination or occlusion. This limitation motivates the design of a proprioceptive membrane that conforms to the surface of interest and infers 3D geometry by reconstructing its own deformation. Conventional deformation-aware membranes typically rely on resistive, capacitive, or magneto-sensitive mechanisms, but can suffer from structural complexity, limited compliance during large-scale deformation, and susceptibility to electromagnetic interference. This work presents a soft, flexible, and stretchable proprioceptive silicone membrane based on optical waveguide sensing. The membrane integrates edge-mounted LEDs and centrally-distributed photodiodes (PDs) within a multilayer elastomeric composite. Rich deformation-dependent light-intensity signals are decoded by a data-driven model to recover the membrane geometry. Real-time reconstruction is demonstrated on a customized 140 mm square membrane at an end-to-end update rate of 90 Hz, achieving an average reconstruction error of 1.307 mm for out-of-plane deformation of up to 25 mm. The proposed sensor also demonstrates accurate reconstruction under large in-plane deformation, achieving reliable shape recovery up to 75% strain with an average Chamfer distance of 1.214 mm. The proposed framework provides a scalable, robust, and low-profile solution for global shape perception in deformable robotic systems.

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